Question

Parallelogram ABCD formed by the line y = hx, y = hx + 1, y = kx and y = kx + 1

Then the area of ABCD ?

a)" "|h-k|/(h-k)^2

b)" "2/|h-k|

c)" "2/|h+k|

d)" "1/|h-k|

Solution

According to the given figure, parallelogram ABCD

Let equation of line AB : y = hx

Equation of line BC: y = kx

Equation of line CD: y = hx + 1

Equation of line DA: y = kx + 1

We need to find the points of intersection of lines in order to get coordinates points.

After simplification we will get,

A(1/(h-k), h/(h-k)), B(0,0), C(1/(k-h), k/(k-h)) and D(0,1)

Area of parallelogram ABCD = (1/2)|(0,0),(1/(k-h), k/(k-h)),(0,1),(1/(h-k), h/(h-k)),(0,0)|

= (1/2)|0 + 1/(k-h) - 1/(h-k)|

= 1/|h-k|